Zhou, Zhan; Yu, Jianshe; Guo, Zhiming Periodic solutions of higher-dimensional discrete systems. (English) Zbl 1073.39010 Proc. R. Soc. Edinb., Sect. A, Math. 134, No. 5, 1013-1022 (2004). The authors consider the second-order discrete system \[ \Delta^2X_{n-1}+ f(n, X_n)= 0,\quad n\in\mathbb{Z},\tag{1} \] where \(f\in C(\mathbb{R}\times \mathbb{R}^m, \mathbb{R}^m)\), \(f(t+ M,\mathbb{Z})= f(t,\mathbb{Z})\) for any \((t,\mathbb{Z})\in \mathbb{R}\times \mathbb{R}^m\) and \(M\) is a positive integer. The existence of \(M\) periodic solutions of (1) is proved. Reviewer: Stefan Balint (Timişoara) Cited in 2 ReviewsCited in 80 Documents MSC: 39A11 Stability of difference equations (MSC2000) 39A12 Discrete version of topics in analysis 34C25 Periodic solutions to ordinary differential equations Keywords:second-order discrete system; periodic solution PDF BibTeX XML Cite \textit{Z. Zhou} et al., Proc. R. Soc. Edinb., Sect. A, Math. 134, No. 5, 1013--1022 (2004; Zbl 1073.39010) Full Text: DOI OpenURL